I can't add a New library in Blender 2.8
Why?
When you try to  create a new library with the add-on, it tries to create a new .blend file and since the add-on's directory is in Program Files folder(if you are on Windows) it does not have permissions to do so and fails.
Solutions
You could run Blender with administrative privileges by right-clicking it and choosing Run as administrator. This way it gains permissions to write the file in the current add-on's folder.
Or even better solotion
You could move the add-on from
C:\Program Files\Blender Foundation\Blender 2.81\2.81\scripts\addons
to
C:\Users\[Your User Name]\AppData\Roaming\Blender Foundation\Blender\2.81\scripts\addons\
where it will be able to write the files when started normally. Note that you have to move the add-on's folder (in this case C:\Program Files\Blender Foundation\Blender 2.81\2.81\scripts\addons\materials_library_vx\), and not copy it since if you had it in both places you would have a conflict.